describes an object shape by harmonics of elliptical Fourier series

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The shape of an object is a closed curve that bounds the object. This curve is named outline.

ElFourier works with vectorized outines. They are the curves which consist of short linear segments connected with each other.

ElFourier reads vector outlines from SVG file

Vector outline

To create a vector outline, you need to load the object image into any vecor editor, trace it by Bezier curves, and save result as a separate SVG.


ElFourier reads SVG file with the vector outline of an object. One file must contain only one outline, the others program ignores.

Many objects

Open as many SVG files as you need. ElFourier can simultaneously works with many outlines.

Harmonics are the numbers which describe geometric features of a two-dimensional object.

Harmonics of different shapes are unique and differ from each other. If we compare harmonics using multidimensional statistical methods, we will learn how the shapes differ.

ElFourier allow adjusting the number of used harmonics

The number of harmonics influences on the reconstructed outline.
The more harmonics you use, the less the difference between the restored and the original outlines. However you can also compare shapes using a small number of harmonics.

ElFourier helps to prepare outlines for reliable comparison

To reliable compare outlines, it is necessary to make the signs of the identical components of the first harmonics equal.

Disordered outlines

Prepared outlines

The identical components of the first harmonics have different signs.

The identical components of the first harmonics have equal signs.

To prepare outlines for reliable comparison

you must: equally arrange their sides, identically orient them, place starting points of outlines in the same positions.

Mirror and rotate outlines to identically arrange their sides.

Relocate starting points to place them in the same positions.

Change outlines orientation to identically orient them all.

To compare shapes by means of harmonics use multivariate statistical methods

Take series of harmonics, corresponded to compared shapes, and apply: principal components analysis, cluster analysis, discriminant analysis, neural network classificator or another classification method that you prefer.

ElFourier has other usefull features

Find invariant harmonics

Program finds harmonics that are independent to the object position, rotation, and sizes.

Align outlines

When program opens an outline, it aligns it along a vertical axis.

Highlight negative harmonic components

It highlight table cells with a negative components of harmonics.

Draw outlines

It draws the silhouette of the original shape and a restored outline over it.

Show outline orientation

It paints outlines oriented counterclockwise.